As others have also said above, I wrap in different dirrections depending on the tape. In most cases I start at the ends and work toward the center so as to avoid curling on the bends. For Benotto tape and, I like to finish with heat and/or super glue for a clean look. For cork or modern tape such as Fizik microtape (my current favorite), I taper the end of the wrap so it has a clean edge at the center. For cloth tape, I go center to end (just like Eddy!) and replace if/when it starts to curl.

It is important to wrap in the clockwise/counterclockwise direction described in the Park Tools link. This is so when you are pulling back on the tops (such as when climbing), you twist the wrap tighter. If you wrap the wrong way, pulling on the tops will help to loosen the wrap.